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Question

If 2 is a zero of the polynomial p(x) and one zero is half of the other zero. Which of the following expressions can p(x) be?

A
p(x)=x26x+5
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B
p(x)=x23x+2
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C
p(x)=x210x+16
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D
p(x)=x26x+8
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Solution

The correct options are
B p(x)=x23x+2
D p(x)=x26x+8

One zero is half the other, the other zero of the polynomial can be either half of 2 or twice of 2.
Other zero can be 1 or 4.

Two polynomials are possible.
They are:

(i) When the two zeroes are 2 and 1
p(x)=(x1)(x2)
p(x)=x23x+2

(i) When the two zeroes are 2 and 4
p(x)=(x4)(x2)
p(x)=x26x+8

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